Method for measuring the distance and/or the relative velocity between two objects

ABSTRACT

A method of measuring the distance between two objects and/or the speed of one object in relation to the other, the objects incorporating respectively a transmitter-receiver unit and a transponder or reflector, in which method a phase comparison is made between a signal transmitted by the transmitter-receiver unit and a signal received in the transmitter-receiver unit and transmitted from the transponder or reflector. In accordance with the invention the transmitter-receiver unit is caused to transmit signals of microwave frequency, preferably about 2450 MHz, this transmission comprising the transmission of a first signal having a first frequency, the transmission of at least one second signal having a higher or lower frequency, and the transmission of a third signal having the same frequency as the first mentioned signal, wherewith the phase differences φ between the transmitted signals are formed, these phase differences corresponding to the distance between the transmitter-receiver unit and the transponder.

The present invention relates to a method of measuring the distanceand/or the relative velocity between two objects. More specifically,although not exclusively, the invention relates to the measurement ofthe distance and/or the relative velocity between a first object and asecond object, of which the first object incorporates atransmitter-receiver unit and the second object incorporates atransponder. The transmitter-receiver unit is constructed to transmit asignal to the transponder and to receive a signal emanating therefrom.

The invention relates specifically to the measurement of distance and/orvelocity by making a phase comparison in the transmitter-receiver unitbetween the signal transmitted to the transponder and the signalreceived therefrom.

The concept of the phase difference method in distance measuringprocesses is well known per se and can be applied with various types oftransmitter-receiver apparatus and transponders or reflectors.

When practising the present invention there is preferably used themethod and apparatus for creating phase differences described, andillustrated in the Swedish patent specification No. . . . (correspondingto Swedish patent application No. 8505888-1), although it will beunderstood that the present invention is not at all dependent on the useof this described and illustrated method and apparatus.

Since a phase difference can only be determined within the range 0-2π,the greatest unambiguous distance R for a given transmitted frequency F1is

    R=c/(2·F1)

where c is the speed of light.

The present invention particularly recommends the use of microwavefrequencies. R_(max) is only 6 cms when using the frequency 2500 MHz.

Another problem associated with measuring methods that rely onphase-differences resides in the difficulties which occur when the twoobjects move in relation to one another, since the phase relationshipsthen change with time.

It is often necessary at times, however, to measure distances underdynamic conditions.

It is also desirable, in many contexts, to be able to determine thelocation of an object, e.g. a motor vehicle, within a restricted areawith a high degree of accuracy, inter alia so as to be able to navigatethe vehicle within this area. One common method of determining theposition of an object in relation to a reference system is to measurethe distance between the object and a number of reference points in thesystem. The position of the object can be readily calculated from thesemeasured distances, with the aid of trigonometrical functions. Theaccuracy to which the position of the object is determined is directlyproportional to the accuracy to which the distance(s) is (are) measured.

These drawbacks and problems are not found with the method according tothe invention, which enables distances to be determined very accurately,even under dynamic conditions, and with which both the distance and theprevailing velocity between the objects can be measured.

Thus, the present invention relates to a method for measuring thedistance between two objects and/or the speed at which they moverelative to one another, said two objects incorporating respectively atransmitter-receiver unit and a transponder or reflector, in whichmethod a phase comparison is made between a signal transmitted by thetransmitter-receiver unit and a signal received thereby from thetransponder or reflector, the method being characterized by transmittingfrom the transmitter-receiver unit signals of microwave frequency,preferably a microwave frequency of about 2450 MHz; transmitting a firstsignal having a first frequency; transmitting a second signal of higheror lower frequency; transmitting a third signal of the same frequency asthe frequency of the first signal; and forming the phase differences φbetween the transmitted signals, these phase differences correspondingto the distance between the transmitter-receiver unit and thetransponder.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in more detail with reference tovarious diagrams shown on the accompanying drawings, in which

FIGS. 1, 3, 4 and 6 are diagrams in which phase difference is plottedagainst frequency;

FIG. 2 is a diagram in which frequency is plotted against time; and

FIG. 5 is a diagram in which phase difference is plotted againstprevailing frequencies when carrying out a multiple of measuringoperations (i).

When measuring distances with the aid of phase-difference measuringtechniques, the phase difference between transmitted and receivedsignals is

    φ=(w.sub.1 ·2R)/c                             (1)

where w₁ is the angular frequency of a signal of frequency F1.

The distance is then ##EQU1##

As beforementioned, the maximum unambiguous distance is ##EQU2##

Provided that a second frequency F2 is used in the measuring process,the distance can be calculated from the relationship ##EQU3##

The maximum unambiguous distance will then be ##EQU4##

The process of measuring at two frequencies F1 and F2 is illustrated inFIG. 1, which shows a diagram relating to the phase difference φ as afunction of the frequency F. The inclination of a line extending betweenthe two measuring points thus determines the distance, as seen from therelationship (4).

The aforesaid will only apply, however, when the distance R is constant.Accuracy increases with increasing frequency differences. Theunambiguous distance, however, decreases.

If the objects move relative to one another, the error in the measureddistance is given by the relationship ##EQU5##

Where v is the relative velocity of the objects and t is the timeinterval between measurements.

This error is eliminated in accordance with the invention by carryingout a further phase measuring process, in addition to the two phasemeasuring processes aforementioned, this further phase measurement beingmade at a lower frequency than the highest frequency F2. It is assumed,by way of example, that the third phase measuring operation is carriedout at the frequency F1 and at the time 2t.

Thus, there is transmitted a first signal having the frequency F1, asecond signal having the frequency F2, which differs from the frequencyF1, and a third signal having the same frequency F1 as the first signal.

Assume that the distance R is changed uniformly with time, in accordancewith the expression

    R(t)=R.sub.o +v·t                                 (6)

where R_(o) is the distance when the time t=0.

Corresponding to expression (1), the phase difference φ₂ deriving fromthe phase measuring process with frequency F2 carried out at time t canbe expressed as ##EQU6##

Similar to the expression (7), φ₃ can be expressed as ##EQU7##

The above is illustrated in FIG. 2, in which straight lines have beendrawn between co-ordinates which constitute the frequency F transmittedat times o, t and 2t.

FIG. 3 illustrates the phase differences φ which occur, as a function ofthe transmitted frequency, in which straight lines have been drawnbetween the measuring points.

The slope of the line L1 in FIG. 3, drawn between the phase differenceswhich occur when measuring with the frequency F1 at time o, and with thefrequency F2 at time t, differs from the slope of the broken ordiscontinuous line L2. The discontinuous line L2 corresponds to the linein FIG. 1. This difference in slope is due to the relative speed of oneobject to the other. The line L3 connects the phase differences whichoccur when measuring with the frequency F2 at the time t, and with thefrequency F1 at the time 2t.

The distance at time t can be determined from the slope of the broken ordiscontinuous line L4.

For this reason there is formed a median value of φ₁ and φ₃, referred toas φ₄ ##EQU8##

The distance is calculated from the equation (4), in which φ₄ isinserted instead of φ₁

It will be seen that when formulating φ₂ -φ₄ in accordance with ##EQU9##the calculated distance is

    R.sub.calc =R.sub.o +v·t,

i.e. the real or true distance at time t.

Thus, the distance is calculated with the aid of the expression##EQU10## which corresponds to the slope of the line L4.

This applies provided that the speed is uniform and that measurementsare taken at uniform intervals of time.

According to the invention, the speed at any given moment can bedetermined by forming the difference between φ₃ and φ₁ ' ##EQU11##

The distance can be readily determined, even when thetransmitter-receiver unit and the transponder move relative to oneanother, by utilizing three phase angles, of which two occur at the samefrequency. The first and the third signal conveniently have a frequencyof preferably 2450 MHz, and the frequency difference between thefrequencies of these signals and the frequency F1 of said second signalis preferably much lower, preferably from 50 kHz to 50 MHz.

According to one preferred embodiment, there are transmitted severalseries of said first, second, and third signals in successive order,where the frequency differences between the second signal F2 and theremaining two signals F1, F1 increase, which corresponds to aprogressively decreasing unambiguous-distance range.

According to another preferred embodiment, at least three series of saidfirst, second, and third signals are transmitted, where the aforesaidfrequency differences increase in accordance with a series which is aneven multiple of the lowest frequency, preferably the series 50 kHz, 500kHz and 5 MHz, as exemplified below.

A high degree of accuracy and a long or wide unambiguous range can behad by carrying out a multiple of measurements according to theaforegoing with progressively decreasing distances, i.e. with aprogressively increasing difference between the frequencies F2 and F1.

A first series of the first, the second, and the third signal can beused, for example, to determine the distance within a range of 300meters, when the effective measuring range is 0-300 meters. In this casethe frequency difference F2-F1 shall be 50 kHz. The frequency F1 maythen be 2450 MHz, for example. A second series of said signals can beused to determine the distance up to a range of 30 meters, in which casethe frequency difference F2-F1 shall be 500 kHz. A third series of thesignals, with a frequency difference of 5 MHz, can be used to determinethe distance to a range of 3 meters, etc. The ultimate degree ofaccuracy is determined by the level of accuracy within the smallestrange, e.g. within the range of 3 meters, corresponding to a frequencydifference of 50 MHz. In the measuring operations carried out previoushereto, the only accuracy required is that of determining the correctrange.

Instead of first transmitting a frequency F1 followed by a higherfrequency F2, which in turn is followed by the first transmittedfrequency F1, the second transmitted frequency F2 may be lower than F1.

According to a preferred embodiment of the invention there is utilized amodified form of the aforedescribed method, this modified method beingcharacterized in that the second signal comprises a first series ofsignals which form a frequency series of progressively risingfrequencies, and a second series of signals which form a frequencyseries of progressively falling frequencies, these series beingtransmitted in succession.

According to one preferred embodiment the difference between twomutually adjacent frequencies is constant in both frequency series,preferably about 50 kHz.

This embodiment of the invention is described below.

The phase difference φ between a transmitted and a received signal as afunction of the transmitted frequency F can be expressed as ##EQU12##

When derivating φF in respect of F, there is obtained ##EQU13##

Analogous with what was said in the aforegoing with regard to therelationship (4), the distance R can thus be determined from the slopeor gradient coefficient of the function φ(F), namely ##EQU14##

The use of solely two points on a curve, as previously described,enables the measuring and calculating process to be effected veryquickly.

The use of several points on a curve, however, enables the gradientcoefficient k to be determined more accurately, because it is thenpossible to form a median value.

This results in the suppression of certain types of disturbance, such asdisturbances caused by reflexion against an extraneous object in thesurroundings, i.e. disturbances of the so-called multiple path type. Thegradient coefficient is namely determined chiefly by the distance forthe strongest signal, which is normally the direct signal.

Phase contributions from signals additional to the direct signals areadded to the direct signals. The remaining signals are manifested asbeats in the measured phase function. A phase function is illustrated inFIG. 4 by a continuous line L5. The indirect signals present behave asbeats, e.g. as illustrated by the discontinuous line L6.

In addition to the use of a multiplicity of points when determining thephase curve resulting in a reduction in the number of errors caused bybeats, it will be understood that the wider the frequency ranges usedthe greater the extent to which the indirect signals are suppressed.

This embodiment of the method also results in an error in the distancemeasurement when the objects move relative to one another, if only, forexample, one rising series of frequencies is transmitted.

Consequently, the present invention recommends the use of two frequencyseries, namely one series of rising frequencies and one series offalling frequencies.

For example, the rising frequency series may be

    F(i)=F.sub.o +idF, where i=0,N                             (17)

and the falling frequency series may be

    F(i)=F.sub.o +N·dF+(N-1)dF, where i=N+1,2N        (18)

The total series thus extends from the frequency F_(o) up to thefrequency F_(o) =NdF, and then down to F_(o), and includes a total of2N+1 measuring processes.

Assume that the phase measurement is carried out at the time interval t₁and that the distance between the objects is a linear function of thetime according to the equation (6).

The phase measured for the frequency series (17) can then be expressedas ##EQU15## which gives ##EQU16##

Correspondingly, the phase measured in respect of the frequency series(18) can be expressed as ##EQU17##

The various phases φ_(i) (F) according to the expression (20) correspondto the line L15 in FIG. 5, and the various phases φ_(i) (F) according tothe expression (21) correspond to the line L16 in FIG. 5.

Values which correspond to the chain line L9 can be obtained, by forminga series of median values of the points φ_(i) (F) corresponding to thelines L7 and L8.

The series can be written as ##EQU18##

The relationship expressed in (22) can also be written as ##EQU19##where i=0,N

According to the relationship (15) the slope or gradient coefficient kis ##EQU20##

The calculated distance according to the relationship (16) is ##EQU21##

which corresponds to the real or true distance at time t=N·t_(i). Thus,the distance is not affected by the speed.

The phase differences φ(F) according to the relationship φSUM; above(22) can therefore be used to calculate the distance R, via acalculation of the gradient coefficient of a straight line on which thevalues φSUM_(i) lie.

The median value of the gradient coefficient k is determined by linearregression according to the lowest root-error-square method in a knownway, or by some other known method of forming median values.

The gradient coefficient k thus obtained is inserted in the aboverelationship or equation (26), and the distance calculated therefrom.

A multiplicity of phase differences are obtained, when measuring inaccordance with the frequency series (17) and (18). The thus measuredphase differences may, for instance, produce phase differences φ such asthose illustrated in FIG. 5, where φ is shown as a function of i, i.e.the frequency that is transmitted on the i:nth transmission. The reasonfor the saw-tooth curve is because the phase difference can be at most2π. Consequently, the phase jump must be straightened with each passageof 2π. This can be effected in accordance with the following algorithm.

When φ_(i+1) -φ_(i) <φ_(v), the value φ_(i+1) shall be substituted forthe value φ_(i+1) =φ_(i+1) +2π, where i=0,N-1.

When φ_(i+1) -φ_(i) >φ_(v), the value φ_(i+1) shall be substituted forthe value φ_(i+1) =φ_(i+1) -2π, where i=N,2N-1.

The angle φ_(v) lies within the range 0-2π and is preferably around zero(0) in the case of static measurements and is selected at higher valueswith increasing velocities v.

φ_(v) is preferably chosen in accordance with the relationship ##EQU22##

Graphically, the aforesaid algorithm corresponds to the continuous curvesections L10--L14 in FIG. 5 straightened to form the chain-line curveL15,L16.

As will be evident from above, FIG. 6 corresponds in principle to FIG.3. The gradient coefficient of the chain line 29 corresponds to thedistance, as beforementioned.

As mentioned above with reference to the relationship or equation (13),the momentary velocity can also be calculated as ##EQU23##

It will therefore be obvious that the second embodiment of the presentinvention affords an extremely accurate result.

However, it is preferred in accordance with a third embodiment of theinvention to apply a combination of measuring operations, in which ameasuring operation according to the first mentioned embodiment iseffected in order to determine the distance range within which thetransponder is located in relation to the transmitter-receiver unit, andin which the last mentioned embodiment is used to determine, withextreme accuracy, the location of the transponder within the rangeestablished. In this way, only a few frequencies need be transmitted inorder to determine, e.g., a range of 3 meters, whereafter a rising orfalling frequency series comprising a smaller number of frequencies istransmitted.

Thus, this combination embodiment enables a lower number of frequenciesto be transmitted while achieving a high degree of accuracy. The totaltime taken to carry out a measurement is also reduced, which is a greatadvantage when the velocity v in the system is high.

Instead of transmitting a first frequency series with risingfrequencies, followed by a second frequency series with fallingfrequencies, there can be transmitted a first frequency series offalling frequencies followed by a second frequency series of risingfrequencies.

It will be evident from the aforegoing that the present inventionovercomes all of the problems mentioned in the introduction andconstitutes an important step forward in the art.

The invention is not restricted to the described and illustratedembodiments, but can be modified within the scope of the followingclaims.

I claim:
 1. A method of measuring the distance between, and/or themutual relative speed, of two objects which respectively include atransmitter-receiver unit and a transponder, and in which method a phasecomparison is made between a signal transmitted from thetransmitter-receiver unit and a signal received in said unit from thetransponder, wherein the transmitter-receiver unit is caused to transmitplural signals of microwave frequency, approximately about 2450 MHz;said transmission of plural signals comprising transmitting a firstsignal having a first frequency; transmitting at least one second signalhaving a higher or a lower frequency than said first signal;transmitting a third signal having the same frequency as said firstmentioned signal; said first, second and third signals being transmittedin succession, all of said first, second and third signals being ofmicrowave frequency as herein set forth, and all of said first, secondand third signals, while transmitted, being continuous wave signalswhereby, for each said transmitted signal a phase difference φ betweenthe transmitted and received signal is formed, which phase differencescorrespond to the distance between the transmitter receiver unit and thetransponder, characterized in that said second signal includes a firstseries of signals that form a frequency series of successively risingfrequencies and a second series of signals that form a frequency seriesof successively falling frequencies, said first series, and said secondseries, being transmitted in succession, whereby a median value (slopeL9) is formed of the respective change of the phase difference with thefrequency (slope L8;L9) that occurs during the series of risingfrequencies and falling frequencies respectively, which median value(slope L9) corresponds to said distance.
 2. A method according to claim1, characterized in that the first and the third said transmittedsignals, both have a frequency of 2450 MHz; and in that the frequencydifferential between the frequency of said first and third transmittedsignals and the frequency of the said second transmitted signal issubstantially lower, and within the range from 50 kHz to 50 MHz.
 3. Amethod according to claim 1, characterized in that the differencebetween two mutually adjacent frequencies in each said series offrequencies is constant, about 50 kHz.
 4. A method according to claim 1,characterized by transmitting in succession a plurality of series ofsaid first, second, and third signals, in which the frequency differencebetween the said second signal and the two remaining signals rises,which corresponds to a successive decrease in the unambiguous distancerange between the objects.
 5. A method according to claim 1,characterized by transmitting in a first stage and in succession aplurality of series of said first, second, and third signals, in whichthe frequency difference between the second signal and the two remainingsignals rises, which corresponds to a successive decrease in theunambiguous distance range between the objects; and by transmitting in asecond stage said two frequency series of successively rising andsuccessively falling frequencies respectively, and determining thedistance between the unambiguous distance range.
 6. A method accordingto claim 4, characterized in that said series of said first, second, andthird signals are at least three in number; and in that said frequencydifferences rise in accordance with a series which is an even multipleof the lowest frequency difference, for example the series 50 kHz, 500kHz and 50 MHz.
 7. A method according to claim 1, characterized byforming the differential between the phase difference that occurs whentransmitting the first transmitted frequency and the phase differencethat occurs when transmitting the last transmitted frequency, which lasttransmitted frequency is equal to the first transmitted frequency, saiddifferential corresponding to the momentary velocity of one object inrelation to the other.